The limits of visual awareness are often attributed to a finite supply of visual attention (Chun & Wolfe, 2001) and processing constraints of the prefronto-parietal network (Dehaene & Changeux, 2011). Here, we investigate the extent to which the limits of visual awareness are related to representational constraints within the higher-level visual system. To measure the limits of visual awareness, we used two different behavioral paradigms that render stimuli invisible. In Experiment 1, we used visual masking to measure how well items from different categories mask one other (e.g., buildings masking cars). In Experiment 2, we used continuous flash suppression to measure how long it takes an item from one category (e.g., a face) to break through suppression by items from another category (e.g., bodies). We then used fMRI to measure the similarity of the neural responses elicited by those categories across the visual hierarchy and used representational similarity analysis (Kriegeskorte & Kievit, 2013) to compare the behavioral and neural results. In both experiments, we found that pairs of categories that strongly mask and suppress each other in behavior also elicit more similar neural response patterns. Brain/behavior correlations were strong within ventral occipital cortex (Exp. 1: r=0.84*; Exp. 2: r=0.64*) and lateral occipital cortex (Exp. 1: r=0.70*; Exp. 2: r=0.73*), weaker within occipitoparietal cortex (Exp. 1: r=0.52*; Exp. 2: r=0.44), and not significant within V1-V3 (Exp. 1: r=0.05; Exp. 2: r=-0.39). Together, these results show that the organization of higher-level visual cortex predicts the degree to which different stimuli will compete for visual awareness. We suggest that this organization imposes a limit on the capacity of visual awareness. Under this view, the extent to which items activate overlapping, capacity-limited neural channels constrains the amount of information that can be accessed by visual awareness.